Aircraft trajectory calculation method, device, model training method and program product

Abstract

The present invention discloses a method, device, model training method, and program product for solving aircraft trajectories, relating to the field of aerospace, and used to simultaneously ensure both aircraft trajectory solution efficiency and physical consistency. The present invention generates a trajectory solution label sample data set by constructing a discretized aircraft trajectory dynamics differential model, and uses the trajectory solution label sample data set to train the flight trajectory solution model. The flight trajectory solution model embeds the constraints of the discretized aircraft trajectory dynamics differential model, and ultimately uses the trained flight trajectory solution model to predict the trajectory state at future time steps. The present invention effectively solves the dual problems of the lack of real-time performance of traditional methods and the poor generalization of pure data-driven models.

Description

Technical Field

[0001] The present invention relates to the field of aerospace technology, and in particular to an aircraft trajectory calculation method and device, an aircraft trajectory calculation model training method, and a computer program product. Background Art

[0002] In the field of aerospace, the effective implementation of key links such as aircraft trajectory planning, trajectory prediction, and online guidance is highly dependent on two core indicators: trajectory state solution accuracy and solution speed. As the core technical foundation for achieving high-precision trajectory planning, reliable trajectory prediction, and real-time online guidance, aircraft trajectory state solution is becoming increasingly important as aircraft performance improves and mission complexity increases. Aircraft trajectory characteristics are usually described as a set of dynamic differential equations containing multiple state variables and strong nonlinear characteristics. For aircraft motion differential equations with multiple state variables and strong nonlinear coupling, high-precision and high-real-time solution is the key technical guarantee for ensuring the safe and reliable operation of aircraft in complex environments.

[0003] In currently known engineering practices, two main methods are used for trajectory solution: traditional methods based on numerical calculations and modern methods based on deep learning.

[0004] Traditional methods, such as the fourth-order Runge-Kutta algorithm, are widely used due to their excellent numerical stability. These methods approximate the solutions to differential equations through a stepwise iteration process, providing reliable solution accuracy in conventional application scenarios. However, with the development of new flight platforms such as hypersonic vehicles, the limitations of these methods have become increasingly prominent. In particular, when dealing with complex aerodynamic characteristics and dynamic problems under extreme flight conditions, traditional numerical methods consume a large amount of computing resources, resulting in significantly longer solution times and making it difficult to meet the stringent millisecond-level response requirements of real-time guidance systems.

[0005] The rapid development of deep learning technology has opened up new possibilities for trajectory calculation. Data-driven neural network models enable rapid inference through forward propagation, demonstrating significant advantages in computational efficiency. However, these approaches suffer from two fundamental flaws: they rely entirely on the statistical properties of the training data and lack explicit modeling of physical laws, potentially leading to calculations that violate fundamental physical laws. Second, in engineering practice, obtaining high-quality flight data covering all operating conditions is extremely challenging, and insufficient data can significantly degrade model generalization performance. These limitations make purely data-driven approaches difficult to reliably apply in safety-critical scenarios.

[0006] For example, Chinese patent publication CN112380692A discloses a "Deep Learning-Based Online Aircraft Trajectory Optimization Method." This method models aircraft trajectory optimization, transforms the optimal control problem into a two-point boundary value problem using the Pontryagin principle, generates a large amount of data through reverse integration, and achieves trajectory optimization through deep learning training. The neural network in this method targets trajectory optimization methods, aiming to solve trajectory control variables. Furthermore, neural network training relies entirely on sample data, which can easily lead to poor model generalization. Another example is Chinese patent publication CN114840019B, which discloses a "Real-Time Aircraft Penetration Trajectory Generation Method and System." This method solves the penetration trajectory optimization problem using a second-order cone programming method, generates a large number of trajectory samples, and trains using a deep neural network method to achieve real-time trajectory generation. This document essentially still addresses the trajectory optimization problem, aiming to solve trajectory control variables. Furthermore, neural network training relies entirely on sample data and does not involve model constraints, which can easily lead to poor model generalization.

[0007] In summary, while traditional numerical methods offer good physical consistency, they lack computational efficiency. On the other hand, while purely data-driven models offer high computational speed, they carry the risk of deviating from physical laws. This dilemma severely constrains the development of modern aircraft trajectory generation technology. In particular, in complex systems like hypersonic vehicles, which feature multiple state variables and strong nonlinear characteristics, existing technologies struggle to simultaneously address the three key requirements of real-time performance, accuracy, and physical consistency. Summary of the Invention

[0008] The object of the present invention is to provide an aircraft trajectory solution method, device, model training method and program product to address all or part of the above-mentioned problems, so as to simultaneously ensure the efficiency and physical consistency of aircraft trajectory solution.

[0009] The technical solution adopted in the present invention is as follows:

[0010] A method for calculating an aircraft trajectory, comprising:

[0011] S1. Construct a discretized differential model of aircraft trajectory dynamics;

[0012] S2. constructing a trajectory solution label sample data set based on the discretized aircraft trajectory dynamics differential model according to the initial state variables and control variable set;

[0013] S3. With the goal of minimizing network loss, a flight trajectory solution model is trained using the trajectory solution label sample data set; the flight trajectory solution model takes the current state variables, control variables, and time as inputs and outputs the state variables at the next time; the network loss includes data-driven loss and physical loss, and the physical loss embeds the constraints of the discretized aircraft trajectory dynamics differential model;

[0014] S4. Utilize the trained flight trajectory calculation model to calculate the state variables at the next moment in real time based on the current state variables, control variables, and time.

[0015] In addition, the present application also provides an aircraft trajectory solution device, which includes a processor and a storage medium, wherein the storage medium stores a computer program, and when the processor runs the computer program, it can execute the above-mentioned aircraft trajectory solution method.

[0016] The present application also provides a computer program product, including a computer program, which executes the above-mentioned aircraft trajectory solution method when executed by a processor.

[0017] On the other hand, the present application also provides an aircraft trajectory solution model training method, which includes:

[0018] S1. Construct a discretized differential model of aircraft trajectory dynamics;

[0019] S2. constructing a trajectory solution label sample data set based on the discretized aircraft trajectory dynamics differential model according to the initial state variables and control variable set;

[0020] S3. With the goal of minimizing network loss, the flight trajectory solution model is trained using the trajectory solution label sample data set; the flight trajectory solution model takes the current state variables, control variables and time as input, and outputs the state variables at the next time; the network loss includes data-driven loss and physical loss, and the physical loss embeds the constraints of the discretized aircraft trajectory dynamics differential model.

[0021] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are:

[0022] This application innovatively integrates physical modeling and deep learning to construct a new, efficient and reliable trajectory calculation method. It proposes embedding the aircraft dynamics equations in a differentiable form within the neural network training process, enabling the network model to adhere strictly to fundamental physical laws while maintaining the efficiency advantages of data-driven methods. This embedded physical constraint design not only significantly improves computational efficiency but also ensures the physical plausibility of the solution results, effectively addressing the dual challenges of the lack of real-time performance of traditional methods and the poor generalization of purely data-driven models. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] The present invention will now be described by way of example with reference to the accompanying drawings, in which:

[0024] Figure 1 This is a flow chart of an aircraft trajectory calculation method in one embodiment of the present application.

[0025] Figure 2 This is a data flow diagram of training a flight trajectory solution model in one embodiment of the aircraft trajectory solution method of the present application.

[0026] Figure 3 This is a three-dimensional comparison diagram of the aircraft trajectory calculated by the aircraft trajectory calculation method of the present application and the aircraft trajectory calculated by the baseline method.

[0027] Figure 4 is with Figure 3 Comparison chart of six state parameters of the aircraft trajectory solved in the same embodiment.

[0028] Figure 5 is with Figure 3 A comparison chart of the solution time of the present application method and the baseline method in the same embodiment, where sub-graph (a) is the present application and sub-graph (b) is the baseline method.

[0029] Figure 6 This is a structural diagram of an aircraft trajectory solving device of the present application in one embodiment.

[0030] Figure 7 This is a flowchart of an aircraft trajectory solution model training method in one embodiment of the present application. DETAILED DESCRIPTION

[0031] All features disclosed in this specification, or all steps in the disclosed methods or processes, except mutually exclusive features and / or steps, can be combined in any manner.

[0032] Any feature disclosed in this specification (including any appended claims and abstract), unless otherwise stated, may be replaced by other equivalent or similar features. In other words, unless otherwise stated, each feature is only an example of a series of equivalent or similar features.

[0033] In response to the problems that traditional aircraft trajectory solution methods have low computational efficiency and purely data-driven neural network models lack reliability due to poor physical consistency, the embodiments of the present application propose an aircraft trajectory solution method, device, model training method and program product. By innovatively integrating physical modeling and deep learning, a new trajectory solution method with both high efficiency and reliability is constructed. While maintaining the advantages of data-driven, the algorithm strictly follows the basic laws of physics, aiming to effectively solve the problems of insufficient real-time performance of traditional algorithms, instability of accuracy and poor physical consistency of purely data-driven models in scenarios with scarce engineering samples.

[0034] like Figure 1 As shown, the aircraft trajectory solution method proposed in the embodiment of the present application includes the following process:

[0035] S1. Construct a discretized differential model of aircraft trajectory dynamics.

[0036] Step S1 is implemented based on the dynamic differential equations of the hypersonic vehicle trajectory calculation model. As mentioned earlier, the trajectory characteristics of an aircraft are typically described as a set of dynamic differential equations containing multiple state variables and strong nonlinear characteristics. By solving this set of dynamic differential equations, the state variables at each time step are obtained, thereby solving the aircraft trajectory.

[0037] As an optional implementation, step S1 includes the following sub-processes:

[0038] S11. Construct a differential model of the aircraft trajectory dynamics.

[0039] In some optional embodiments of the present application, the aircraft trajectory dynamics differential model is constructed in the form of an aircraft trajectory solution model dynamics differential equation, which can be extended to apply to key areas such as hypersonic aircraft trajectory planning, trajectory prediction and online guidance.

[0040] The differential model of the vehicle trajectory dynamics is constructed as follows:

[0041] Formula (1): ;

[0042] Parameters in the formula:

[0043] Geocentric distance ,longitude ,latitude There are three parameters describing the position of the aircraft; the speed , track angle , heading angle are three parameters describing the aircraft speed. These six parameters together constitute the aircraft trajectory state variables, which are the state parameters required to calculate the aircraft trajectory. In the embodiment of this application, the format of the state variables is uniformly expressed as , That is, it represents the state variable. is the aircraft roll angle; represents the gravitational acceleration of the Earth, where is the equatorial radius of the Earth, is the acceleration due to gravity on the Earth's surface. and are the Coriolis acceleration caused by the Earth's rotation, 、 and is the centripetal acceleration caused by the Earth's rotation. Specifically,

[0044] Formula (2): ;

[0045] in, is the angular velocity of the Earth's rotation.

[0046] and are lift acceleration and drag acceleration respectively.

[0047] Formula (3): ;

[0048] Formula (4): ;

[0049] in, is the mass of the aircraft; is the reference area; taking the unpowered hypersonic gliding reentry vehicle as an example, , ; is the pneumatic pressure; is the atmospheric density, , is the air density, usually taken as ; is the atmospheric standard altitude, usually taken as ; is the altitude; and They are the lift coefficient and the drag coefficient, respectively, and are determined by the angle of attack and Mach number Sure.

[0050] Formula (5): .

[0051] In the continuous state, the differential model of the vehicle trajectory dynamics is expressed as:

[0052] Formula (6): ;

[0053] in, represents the dependent variable of the differential model of the vehicle trajectory dynamics, Indicates about The mapping relationship; represents a six-dimensional continuous state variable; Indicates time; In the field of hypersonic gliding reentry vehicle trajectory optimization, trajectory prediction and guidance, the bank angle is usually and angle of attack As the control variable of the aircraft trajectory, .

[0054] When the initial state variables (i.e., initial trajectory state) and control variables are known, the trajectory state can be obtained by solving the aircraft trajectory dynamics differential model shown in formula (6).

[0055] S12. Use the finite difference method to discretize the differential model of the aircraft trajectory dynamics (i.e., formula (6)).

[0056] Discretization is to perform discrete sampling on a continuous time line, Discretization.

[0057] Specifically, assuming the sampling time step is , the continuous time Discretized into:

[0058] Formula (7): ;

[0059] is the number of time-discrete nodes sampled for a single trajectory, Indicates the node number, which is also the time step number. Indicates the k The moment of the first time step can be called the k moment or time k .

[0060] Corresponding to the discretized sampling time nodes, the discrete trajectory state variables on the aircraft trajectory are , For the k The state variables at the moment, each element of which corresponds to In the k The discrete trajectory control variable is , similarly, For the k The control variables at the moment, each element of which corresponds to In the k The value at the moment.

[0061] Through this discretization process, the aircraft trajectory dynamics differential model shown in formula (6) can be converted into the discretized aircraft trajectory dynamics differential model shown in formula (8).

[0062] Formula (8): ;

[0063] in, Indicates that it is about The mapping relationship of Discretized vehicle trajectory dynamics differential model expression; Represents state variables The differential equations of the trajectory dynamics of the aircraft.

[0064] S2. Based on the initial state variables and control variable sets, a trajectory solution label sample data set is constructed based on the discretized aircraft trajectory dynamics differential model.

[0065] The data used as label samples are the actual values ​​in the aircraft trajectory, which can be obtained by solving the aircraft trajectory through traditional algorithms.

[0066] As an optional implementation, a method for constructing a trajectory solution label sample data set based on a discretized aircraft trajectory dynamics differential model includes:

[0067] S21. Based on the initial state variables, according to the current state variables and each set of control variables in the control variable set, the discretized aircraft trajectory dynamics differential model is iteratively solved by the fourth-order Runge-Kutta numerical integration method to obtain the state variables at each subsequent moment.

[0068] The initial state variable is the only given state variable. The state variable at the initial moment, and the state variable at each subsequent moment, are calculated using the fourth-order Runge-Kutta numerical integration method. The control variable set may include multiple sets of control variables, each of which generates a corresponding aircraft trajectory. In other words, each set of control variables, based on the sampled time series, yields a sequence of state variables.

[0069] Specifically, enter the current time State variables , current moment control variables , and the integration step size (That is, with the next moment k+1 The time difference of the next moment can be solved by the fourth-order Runge-Kutta numerical integration method. k+1 The trajectory state variable The solution method using the fourth-order Runge-Kutta numerical integration method can be expressed as:

[0070] Formula (9): .

[0071] By using the above method, the state variables at the next moment can be calculated given the state variables, control variables, and integration step size at the current moment. The calculated state variables, together with the control variables and integration step size at the next moment, are then brought into formula (9) to calculate the state variables at the next moment. This cycle is repeated to calculate all sampling moments ( N time steps) of the state variables.

[0072] S22. Construct the state variables, control variables, time steps at each moment and the state variables corresponding to the next moment into a trajectory solution label sample data.

[0073] The purpose of model training is to quickly infer the state variables at the next moment. Therefore, the state variables at the next moment are used as the state variables, control variables, and true labels for time step inference at the current moment. Formally, each trajectory solution label sample data is constructed as ,in ; , is the number of control variable groups in a given set of control variables. In the embodiments of the present application, the set of control variables can be obtained using an existing trajectory optimization algorithm, such as the algorithm described in the background section. The specific algorithm used is not limited in the embodiments of the present application; the only requirement is that the set of control variables is ultimately obtained.

[0074] S3. With the goal of minimizing network loss, a flight trajectory solution model is trained using a dataset of trajectory solution label samples. This flight trajectory solution model takes the current state variables, control variables, and time as inputs and outputs the state variables at the next time. Network loss includes data-driven loss and physical loss, with the physical loss embedded in the constraints of the discretized vehicle trajectory dynamics differential model.

[0075] As we can see from the previous text, the state variables that need to be inferred involve state parameters of multiple dimensions, namely the distance from the center of the earth ,longitude ,latitude , speed , track angle and heading angle . If a multi-dimensional neural network model is used, it is highly likely that only an inference model that takes into account the accuracy of each dimension as a whole can be obtained, and it is difficult to ensure the inference accuracy of each dimension. To avoid this phenomenon, in some optional implementations of the present application, the flight trajectory solution model is constructed as a distributed network structure, which includes multiple sub-models, and each sub-model is only responsible for inferring one state parameter. The flight trajectory solution model includes sub-models whose number corresponds to the dimensions of the state variables. Each sub-model takes the current state variable, control variable and time as input, and outputs one dimension of the state variable.

[0076] like Figure 2 As shown in Figure 1, the state variables include state parameters of 6 dimensions, and the flight trajectory solution model includes 6 sub-models, namely, the geocentric distance network, the longitude network, the latitude network, the speed network, the track angle network and the heading angle network. The input layers of the 6 sub-models are all based on the state variables. , control variables and time As input, where Indicates the P Under the group control variables k The distance from the center of the earth corresponding to the moment, the other state parameters and control parameters are the same. Indicates the use of P When the group controls the variables k The geocentric distance network is used to infer the geocentric distance at the next moment. , the longitude network is used to infer the longitude of the next moment , the latitude network is used to infer the latitude of the next moment , the speed network is used to infer the speed of the next moment , the track angle network is used to infer the track angle at the next moment , the heading angle network is used to infer the heading angle at the next moment The state parameters inferred by the final output layer of each sub-model are combined and output in the order of the state parameters of each dimension in the input state variable to obtain the state variable at the next moment. .

[0077] Each sub-model has the same network structure. For example, in some optional embodiments, the sub-model network structure is constructed as follows: an input layer, six hidden layers, and an output layer; each hidden layer includes 64 neurons; adjacent layers are fully connected; and the activation function is the Tanh function.

[0078] When training the flight trajectory solution model, an iterative training method is used until the model converges (or the maximum number of iterations is reached). Figure 2 As shown, the network loss of the flight trajectory solution model Including data-driven losses and physical losses The data-driven loss is a loss that relies solely on the statistical laws of the data, while the physical loss is a loss that is embedded in the constraints of the discretized vehicle trajectory dynamics differential model, which is used to constrain the model to strictly follow the laws of physics.

[0079] Specifically, if Figure 2 As shown in Figure 2, the loss function of the flight trajectory solution model is expressed as:

[0080] Formula (10): ;

[0081] in, Represents network loss, which is data-driven loss and physical losses The composite loss function is composed of two parts. According to the definition above, Respectively indicate the use of P When group control variables are k+1 The predicted state variables and the actual state variables at the moment; Indicates the use of P When group control variables are k+1 The label of the control variable at time. Indicates about The discretized aircraft trajectory dynamics differential model is the true value calculated in step S2. Represents state variables The derivative of can be obtained by automatically differentiating after inference through the flight trajectory solution model.

[0082] The trajectory solution labeled sample data set can be split into a training set and a test set. The training set is used to optimize the network parameters of the flight trajectory solution model, and the test set is used to test and verify the performance of the optimized flight trajectory solution model. During the training process, the Adam algorithm can be used to configure the model and optimize the network parameters.

[0083] In addition, as a preferred embodiment, before using the trajectory solution label sample data set to train the flight trajectory solution model, the data in the trajectory solution label sample data set can also be normalized to improve the training efficiency of the network.

[0084] Since each sub-model is trained and predicted independently, in each round of iteration, each sub-model can independently optimize its own network parameters, thereby specifically improving the inference accuracy of the state parameters of each dimension.

[0085] S4. Utilize the trained flight trajectory calculation model to calculate the state variables at the next moment in real time based on the current state variables, control variables, and time.

[0086] Once the flight trajectory calculation model is trained, it can be deployed in the desired scenario as an intelligent trajectory calculation agent. The aircraft uses the trajectory calculation model to calculate the next flight state (i.e., state variables) in real time based on the current flight state variables, control variables, and time (point in time). This iterative cycle allows the calculation of the entire trajectory. This provides a feasible solution for real-time trajectory calculation in areas such as aircraft trajectory planning, trajectory prediction, and online guidance.

[0087] The performance of the proposed method is also verified in the examples of this application. The RK4 algorithm (fourth-order Runge-Kutta numerical integration method) is selected as the baseline algorithm for accuracy comparison. Figure 3 and Figure 4 As shown, the proposed method (OURS) has similar calculation accuracy compared with the RK4 algorithm, which also proves that the proposed method strictly follows the physical laws and has excellent physical consistency. However, since the proposed method uses a neural network model for inference and calculation, its efficiency in calculating the aircraft trajectory is much higher than that of the RK4 algorithm, and the calculation time can be reduced by at least one order of magnitude. Figure 3 and Figure 4 The solution time of this application and RK4 algorithm is shown in Table 1, and the simulation parameters and indicators are as follows Figure 5 shown.

[0088] Table 1 Comparison of solution time between this application and RK4 algorithm

[0089]

[0090] As shown in Table 1, the solution method of this application achieves a speed improvement of more than 40 times compared with the RK4 algorithm under the same solution conditions.

[0091] According to the concept of the present application, an embodiment of the present application also provides an aircraft trajectory solution device, which includes a processor and a storage medium, wherein the storage medium stores a computer program. When the processor runs the computer program, it can execute the aircraft trajectory solution method of the above embodiment.

[0092] like Figure 6 As shown, in some specific embodiments, the processor and storage medium are connected via a bus. The device also includes an interface circuit, and connections between internal devices within the device and external devices are implemented through the interface circuit. The storage medium can be a non-volatile storage medium such as a magnetic disk, an optical disk, or a ROM (Read Only Memory).

[0093] In addition, an embodiment of the present application also provides a computer program product, which includes a computer program. When the computer program is run by a processor, it executes the above-mentioned aircraft trajectory solution method.

[0094] On the other hand, the embodiment of the present application also provides an intermediate product of an aircraft trajectory solution method, namely, an aircraft trajectory solution model training method, such as Figure 7 As shown, the method includes the following processes:

[0095] S1. Construct a discretized differential model of aircraft trajectory dynamics.

[0096] S2. Based on the initial state variables and control variable sets, a trajectory solution label sample data set is constructed based on the discretized aircraft trajectory dynamics differential model.

[0097] S3. With the goal of minimizing network loss, a flight trajectory solution model is trained using a dataset of trajectory solution label samples. This flight trajectory solution model takes the current state variables, control variables, and time as inputs and outputs the state variables at the next time. Network loss includes data-driven loss and physical loss, with the physical loss embedded in the constraints of the discretized vehicle trajectory dynamics differential model.

[0098] It can be seen from the above steps that steps S1 to S3 in the aircraft trajectory solution model training method are the same as steps S1 to S3 of the previous aircraft trajectory solution method. Therefore, for steps S1 to S3 in the aircraft trajectory solution model training method, the technical features that can be designed can correspond to the optional implementation methods further defined by steps S1 to S3 of the previous aircraft trajectory solution method, and will not be repeated here.

[0099] In general, compared with the prior art, this application has the following characteristics:

[0100] (1) To solve the problem of aircraft trajectory calculation, this application adopts embedded physical constraint neural network technology, and through the dual drive of "data + model", it ensures the generalization performance of the intelligent model and reduces data dependence, and establishes an intelligent trajectory calculation model that integrates flight dynamics. This application can make up for the shortcomings of the traditional fourth-order Runge-Kutta numerical integration method in terms of computational efficiency, and provides a new technical path for the real-time trajectory calculation problem in the fields of aircraft trajectory planning, trajectory prediction and online guidance, and is expected to promote technological progress in related fields.

[0101] (2) In response to the multivariable characteristics of the differential model of hypersonic vehicle dynamics, this application designs a distributed parallel embedded physical constraint neural network architecture. Different trajectory state parameters correspond to independent sub-models. The outputs of each sub-model are merged to obtain the state variable at the next moment. This method achieves a decoupled mapping of different trajectory states, effectively improving network training efficiency and inference accuracy.

[0102] The present invention is not limited to the aforementioned specific embodiments, but extends to any new features or any new combination disclosed in this specification, as well as any new method or process steps or any new combination disclosed.

Claims

1. A method for calculating an aircraft trajectory, characterized in that: include: S1. Constructing a discretized aircraft trajectory dynamics differential model, including: S11. Constructing an aircraft trajectory dynamics differential model; S12. Discretizing the aircraft trajectory dynamics differential model using a finite difference method; S2. Based on the initial state variables and control variable sets, a trajectory solution label sample data set is constructed based on the discretized aircraft trajectory dynamics differential model, including: S21. Based on the initial state variables, according to the current state variables and each group of control variables in the control variable set, the discretized aircraft trajectory dynamics differential model is iteratively solved by a fourth-order Runge-Kutta numerical integration method to obtain the state variables at each subsequent moment; S22. The state variables, control variables, time step at each moment, and the state variables corresponding to the next moment are constructed as a trajectory solution label sample data; S3. With the goal of minimizing network loss, the flight trajectory solution model is trained using the trajectory solution label sample data set, the flight trajectory solution model including sub-models corresponding in number to the dimensions of the state variables; the network structure of each sub-model is the same; each sub-model takes the current state variable, control variable and time as input, and outputs one dimension of the state variable respectively; the flight trajectory solution model takes the current state variable, control variable and time as input, and outputs the state variable at the next time; the network loss includes data-driven loss and physical loss; the physical loss embeds the constraints of the discretized aircraft trajectory dynamics differential model, including: the physical loss embeds the constraints of the discretized aircraft trajectory dynamics differential model by integrating the degree to which the aircraft trajectory dynamics differential results of each set of control variables in the control variable set at each time deviate from the actual value; The loss function of the flight trajectory solution model is designed as: Where, Indicates network loss; represent data-driven losses and physical losses, respectively; Represents the number of discrete points on a single flight trajectory; Indicates the number of control variable groups in the control variable set; Indicates the use of P When the group controls the variables k+1 time; Respectively indicate the use of P When group control variables are k+1 The predicted state variables and the actual state variables at the moment; Indicates the use of P When group control variables are k+1 The labels of the control variables at the time instant; Represents state variables The derivative of Indicates about Discretized differential model of aircraft trajectory dynamics; S4. Utilize the trained flight trajectory calculation model to calculate the state variables at the next moment in real time based on the current state variables, control variables, and time.

2. The method for calculating the trajectory of an aircraft according to claim 1, wherein: The network structure of the sub-model is constructed as follows: It consists of an input layer, 6 hidden layers, and an output layer in sequence; each hidden layer contains 64 neurons; adjacent layers are fully connected; the activation function is the Tanh function.

3. An aircraft trajectory calculation device, characterized in that: The method comprises a processor and a storage medium, wherein the storage medium stores a computer program. When the processor runs the computer program, the method for solving the aircraft trajectory as described in any one of claims 1 to 2 can be executed.

4. A computer program product comprising a computer program, characterized in that When the computer program is executed by a processor, the aircraft trajectory calculation method according to any one of claims 1 to 2 is executed.

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